Dynamic equilibrium
In a sealed bottle of water, water keeps evaporating and vapour keeps condensing. Eventually both happen at the same rate, and the amount of liquid and vapour stays constant. This is equilibrium.
Equilibrium is dynamic: the forward and reverse processes never stop; they just balance. It can be reached from either direction, and only in a closed system.
Example. For H₂(g) + I₂(g) ⇌ 2HI(g), starting with H₂ and I₂, or with HI alone, gives the same equilibrium mixture at a given temperature.
The law of mass action and Kc
For a general reaction aA + bB ⇌ cC + dD, at equilibrium
Kc = [C]ᶜ[D]ᵈ ⁄ [A]ᵃ[B]ᵇ
where square brackets are molar concentrations at equilibrium.
Pure solids and liquids are left out of the expression; their "concentration" is constant.
K depends only on temperature, not on initial concentrations, pressure or catalysts.
For the reverse reaction, K′ = 1/K. If the equation is multiplied by n, K becomes Kⁿ.
For gases, partial pressures can be used: Kp = Kc (RT)^Δn, where Δn = moles of gaseous products − moles of gaseous reactants. If Δn = 0, Kp = Kc.
What K tells us
Value of K | Meaning |
|---|---|
K > 10³ | products dominate; the reaction nearly goes to completion |
10⁻³ < K < 10³ | appreciable amounts of both reactants and products |
K < 10⁻³ | reactants dominate; the reaction hardly proceeds |
The reaction quotient Q has the same form as K but uses concentrations at any moment.
Q < K: the reaction moves forward.
Q > K: the reaction moves backward.
Q = K: it is at equilibrium.
The link with Gibbs energy: ΔG = ΔG° + RT ln Q, and at equilibrium ΔG° = −RT ln K.
Le Chatelier's principle
If a system at equilibrium is disturbed by a change in concentration, pressure or temperature, it shifts in the direction that counteracts the change.
Change | Effect |
|---|---|
Add a reactant (or remove a product) | shifts forward |
Increase pressure (decrease volume) | shifts towards fewer moles of gas |
Increase temperature | shifts in the endothermic direction; K changes |
Add a catalyst | reaches equilibrium faster; no shift, K unchanged |
Add an inert gas at constant volume | no shift |
Example: the Haber process. N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ/mol. High pressure favours ammonia (4 moles of gas → 2). Low temperature favours it too (exothermic), but makes the reaction slow, so a moderate temperature of about 700 K is used with an iron catalyst.
Acids and bases
Concept | Acid | Base |
|---|---|---|
Arrhenius | gives H⁺ in water | gives OH⁻ in water |
Brønsted-Lowry | proton donor | proton acceptor |
Lewis | electron pair acceptor (BF₃, AlCl₃, H⁺) | electron pair donor (NH₃, H₂O, OH⁻) |
In Brønsted-Lowry theory, an acid and the base formed when it loses a proton are a conjugate acid-base pair: HCl and Cl⁻, NH₄⁺ and NH₃. A strong acid has a weak conjugate base.
Ionic product of water and pH
Water ionises slightly: H₂O ⇌ H⁺ + OH⁻. Its ionic product is
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 298 K.
pH = −log[H⁺] and pOH = −log[OH⁻], so pH + pOH = 14 at 298 K.
Example. For 0.001 M HCl, [H⁺] = 10⁻³ M and pH = 3. For 0.01 M NaOH, [OH⁻] = 10⁻² M, pOH = 2 and pH = 12.
Weak acids and bases
A weak acid HA ionises only partly: HA ⇌ H⁺ + A⁻, with Ka = [H⁺][A⁻]/[HA]. The larger Ka (smaller pKa = −log Ka), the stronger the acid.
If the concentration is c and the degree of ionisation α is small, Ka ≈ cα² and [H⁺] = cα = √(Ka c).
Example. Acetic acid, Ka = 1.8 × 10⁻⁵, at 0.05 M: [H⁺] = √(1.8 × 10⁻⁵ × 0.05) = √(9 × 10⁻⁷) ≈ 9.5 × 10⁻⁴ M, so pH ≈ 3.02.
For a conjugate pair, Ka × Kb = Kw.
Common ion effect: adding a salt with an ion common to a weak electrolyte suppresses its ionisation. Adding sodium acetate to acetic acid reduces [H⁺].
Buffers
A buffer solution resists changes in pH when small amounts of acid or base are added. It is made of a weak acid and its salt (acetic acid + sodium acetate) or a weak base and its salt (NH₄OH + NH₄Cl). Blood is buffered at pH about 7.4.
Henderson equation: pH = pKa + log([salt]/[acid]).
Solubility product
For a sparingly soluble salt in equilibrium with its ions, such as AgCl(s) ⇌ Ag⁺ + Cl⁻:
Ksp = [Ag⁺][Cl⁻]
If the solubility is S mol/L, then for AgCl, Ksp = S². For a salt like CaF₂ ⇌ Ca²⁺ + 2F⁻, Ksp = S(2S)² = 4S³.
A precipitate forms when the ionic product exceeds Ksp. The common ion effect lowers solubility, which is used to purify common salt by passing HCl gas through its solution.
Summary
Equilibrium is dynamic; Kc depends only on temperature; Kp = Kc(RT)^Δn.
Compare Q with K to predict direction; ΔG° = −RT ln K.
Le Chatelier: systems counteract imposed changes; catalysts don't shift equilibrium.
pH = −log[H⁺]; Kw = 10⁻¹⁴; buffers resist pH change; precipitation when ionic product > Ksp.